Edge windowing of ofdm based systems

ABSTRACT

Various methods and systems are provided for edge windowing of orthogonal frequency division multiplexing (OFDM) systems. In one example, among others, a method includes obtaining an edge windowing portion by reducing a cyclic prefix size for a quantity of edge subcarriers in an OFDM symbol and reducing side lobes by applying a windowing function to the edge subcarriers. In another example, a device includes a separator capable of dividing subcarriers of an OFDM symbol into first and second subcarrier groups, a first CP adder capable of obtaining a windowing portion by adjusting a cyclic prefix size of the first subcarrier group, and a first windower capable of reducing side lobes by applying a windowing function to the first subcarrier group. In another example, a method includes determining a RMS delay spread of a mobile station and scheduling a subcarrier based at least in part upon the RMS delay spread.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to copending U.S. provisionalapplication entitled, “Edge Windowing of OFDM Based Systems,” havingSer. No. 61/561,015, filed Nov. 17, 2011, which is entirely incorporatedherein by reference.

BACKGROUND

Orthogonal frequency division multiplexing (OFDM) is a signaling schemethat may be used for cognitive radios and spectrum aggregationtechniques. However, rectangular windowing of OFDM symbols produces highside lobes, which results in adjacent channel interference (ACI). Itwould be desirable to reduce the ACI while maintaining a high level ofspectrum efficiency for OFDM based systems.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the present disclosure can be better understood withreference to the following drawings. The components in the drawings arenot necessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present disclosure. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1( a) is a graphical representation illustrating conventionalwindowing of OFDM symbols.

FIGS. 1( b) and 1(c) are graphical representations illustrating edgewindowing of OFDM symbols in accordance with various embodiments of thepresent disclosure.

FIG. 2 is a graphical representation of an OFDM symbol includingsubgroups of edge subcarriers in accordance with various embodiments ofthe present disclosure.

FIG. 3 is a graphical representation of an example of a device 300capable of handling OFDM signaling in accordance with variousembodiments of the present disclosure.

FIG. 4 is an example of the average error vector magnitude (EVM) onsubcarriers in accordance with various embodiments of the presentdisclosure.

FIGS. 5( a) and 5(b) are examples of the suppression performance of edgewindowing relative to the non-windowed OFDM in accordance with variousembodiments of the present disclosure.

FIG. 6 includes graphical representations illustrating edge windowing ofOFDM symbols in accordance with various embodiments of the presentdisclosure.

FIG. 7 illustrates scheduling of subcarriers of an OFDM symbol inaccordance with various embodiments of the present disclosure.

FIGS. 8, 9, 10A-10C, 11A-11C, and 12 are simulation results illustratingthe performance of the edge windowing with scheduling of the subcarriersin accordance with various embodiments of the present disclosure.

FIG. 13A is a flow chart providing an example of edge windowing of OFDMsymbols in accordance with various embodiments of the presentdisclosure.

FIG. 13B is a flow chart providing an example of scheduling subcarriersof OFDM symbols in accordance with various embodiments of the presentdisclosure.

FIG. 14 is a schematic block diagram illustrating an example of thedevice of FIG. 3 in accordance with various embodiments of the presentdisclosure.

DETAILED DESCRIPTION

Disclosed herein are various embodiments of methods related to edgewindowing of orthogonal frequency division multiplexing (OFDM) basedsystems. Adaptive windowing of the orthogonal frequency divisionmultiplexing (OFDM) signals may be used to shape the spectrum of thetransmitted signal, thereby limiting interference of adjacent bands.

In conventional windowing, the same windowing is applied to allsubcarriers of an OFDM symbol. As illustrated in FIG. 1( a), the OFDMsymbol includes a data portion 106 (over period N_(D)) and a cyclicprefix 109 (over period N_(CP)) to eliminate intersymbol interference(ISI) and intercarrier interference (ICI). In addition, an extrawindowing time (or sample period) N_(W) 112 is added between the twoconsecutive ODFM symbols 103. The transition between two consecutiveODFM symbols 103 during N_(W) 112 is smoothed by windowing in order tosuppress the side lobes. While the subcarriers of the previous OFDMsymbol 103 a fade out over N_(W) 112, the subcarriers of the next OFDMsymbol 103 b fade in over N_(W) 112. Since the cyclic prefix 109 anddata part 106 of the OFDM symbol remain, there is no ISI problem.However, the added windowing time 112 of the OFDM signals 103 reducesthroughput performance of the system.

Consider an OFDM symbol 103 with N available subcarriers, N_(CP) cyclicprefix size, T_(S) symbol duration, and N_(G) guard carriers. The smoothtransition can be provided with point-to-point multiplication of thewindowing function and the OFDM symbol extended with a postfix (e.g.,adding N_(W) samples from the beginning of the OFDM symbol 103 to theend of the OFDM symbol 103) and/or a prefix (e.g., adding N_(CP)+N_(W)samples from the last of the OFDM symbol 103 to the beginning of theOFDM symbol 103). As can be seen from FIG. 1( a), only N_(W) samplesfrom the last part of the previous OFDM symbol 103 a and N_(W) samplesfrom the beginning part of the next OFDM symbol 103 b are overlapped tomaintain the orthogonality. Since the duration of the windowed OFDMsymbol 103 is N_(D)+N_(CP)N_(W), conventional windowing decreases thespectrum efficiency of the OFDM symbol 103 depending on N_(W) 112. Onthe other hand, since the cyclic prefix 109 and data part 106 of theOFDM symbol 103 remain, there is no ISI problem due to the multipathdelay spread.

Throughput of the system can be improved by reducing or eliminating theextra windowing time N_(W) 112 between OFDM symbols 103. The subcarrierslocated in the middle of the band (or inner subcarriers) have lessimpact on the side lobes compared to the subcarriers along the edges (oredge subcarriers), since the subcarriers spread as sinc function infrequency domain. Thus, the smooth transition between consecutive OFDMsymbols 103 can be achieved by considering mostly the edge subcarriersfor windowing operation. Because edge subcarriers of the OFDM symbol 103have a larger effect on the side lobes of the OFDM symbol than innersubcarriers, the edge subcarriers may be windowed without comparablewindowing of the inner subcarriers. Accordingly, windowing can beheavily applied to the edge subcarriers over N_(W) and the windowingsize of the inner subcarriers may be decreased to N^(inner) _(W)<N_(W)or eliminated.

With reference to FIG. 1( b), windowing of the edge subcarriers 115 maybe carried out with a smoother transition to reduce the side lobeswithout windowing the inner subcarriers 118. The length (or size) of thecyclic prefix 109 of the edge subcarriers 115 is reduced from N_(CP) toN^(edge) _(CP) to obtain a windowing portion N^(edge) _(W) within thecyclic prefix 109 of the inner subcarriers 118. The size of the cyclicextensions of the inner subcarriers 118 remain as N_(CP). As illustratedin FIG. 1( b), windowing is then carried out on the edge subcarriers 115with smoothing taking place during the windowing portion N^(edge) _(W).In this way, _(W) 112 may be reduced or eliminated, which achieves bothimproved spectrum efficiency and the side lobe suppression at the sametime.

With reference to FIG. 1( c), different windowing functions may beapplied to the edge subcarriers 115 and inner subcarriers 118. Thelength (or size) of the cyclic prefix 109 of the inner subcarriers 118is reduced from N_(CP) to N^(inner) _(CP) to obtain a windowing portionN^(inner) _(W) within the cyclic prefix 109. The size of the cyclicextensions of the edge subcarriers 115 are reduced to N^(edge)_(CP)<N_(CP). Subsequently, the remaining parts from the cyclicextensions are utilized for the windowing of edge subcarriers asN^(edge) _(W)=N_(CP)+N^(inner) _(W)−N^(edge) _(CP). As such, windowingof the edge subcarriers 115 may be carried out with a smoothertransition to reduce the side lobes, while windowing with a sharpertransition may be carried out on the inner subcarriers 118. By windowingthe edge subcarriers 115 over a portion of the cyclic prefix 109, theextra windowing time N_(W) 112 can be reduced to N_(D)+N_(CP)+N^(inner)_(W) as shown in FIG. 1( b), which increases throughput of the system.

Edge windowing provides the advantage of maintaining the spectrumefficiency of OFDM while achieving side lobe suppression. Additionally,edge windowing reduces the windowing time over conventional windowingand may also remove the need for guard bands. A better spectrum shapingcan be provided by increasing S. However, if Si increases, the number ofinner subcarriers 118 which have larger cyclic extension sizesdecreases. This may also introduce ISI and ICI on the subcarrierdepending on the channel dispersiveness. Also, increasing N^(edge) _(W)for a given time period of two consecutive OFDM symbols 103 can resultin better side lobe suppression. However, it can cause more ICI and ISI,since it reduces the cyclic extension sizes of the edge subcarriers 115.

The ICI is caused by the first N^(edge) _(W) samples of the edgesubcarriers 115. This portion constitutes the combination of twoconsecutive OFDM symbols 103 as in FIG. 1( b). Since the time distancebetween main parts of the two sequential OFDM symbols 103 is still morethan N_(CP) and the edge subcarriers 115 of previous OFDM symbol 103fade out in the windowing period, the power of the observed ICI on theinner subcarriers 115 will be mitigated by the characteristics ofwindowing function being used. Since edge windowing is applies thewindowing function to OFDM based systems, different windowing functionsmay be used with edge windowing. Numerous windowing functions that maybe used to suppress the side lobes include, e.g., raised-cosine,trapezoidal, cosine, Tukey windowing functions, etc. Edge windowing maybe applied not only to OFDM based systems (e.g., OFDM and OFDMA) butalso to other OFDM-like systems such as, e.g., single carrier frequencydivision multiple accessing.

As illustrated in FIG. 1( b), it is possible to make N^(inner) _(W)=0.In that case, no windowing is utilized for inner subcarriers 118 byrelying on only the side lobe suppression of the edge subcarriers 115.This approach may maximize the spectral efficiency of the OFDM. If themaximum excess delay spread is equal or less than N^(edge) _(CP),neither ISI nor ICI is observed on both edge subcarriers 115 and innersubcarriers 118. In contrast, if the maximum excess delay spread islarger than N^(edge) _(CP), both ISI and ICI can be observed in the edgesubcarriers 115. In addition, since the orthogonality is lost betweenthe edge subcarriers 115 and inner subcarriers 118, only ICI is observedat inner subcarriers 118. The impact of the ICI caused by the edgesubcarriers 115 becomes weaker for the inner subcarriers 118.

The edge subcarriers 115 and inner subcarriers 118 may be grouped (ordivided up) in a variety of ways. For example, the subcarriers of theOFDM symbol 103 may be equally divided between inner subcarriers 118 andedge subcarriers 115 (e.g., 256 subcarriers with 128 edge carriers and128 inner carriers) on the right and left sides of the inner subcarriers118. Other groupings of the subcarriers are equally applicable as can beunderstood. The edge subcarriers 115 include an equal number ofsubcarriers (S) on either side of the inner subcarriers 118 (e.g., 64subcarriers on either side). In addition, the edge subcarriers 115 maybe divided into subgroups on either side of the inner subcarriers 118.For example, as illustrated in FIG. 2, an OFDM symbol 103 may be dividedbetween a plurality of inner subcarriers 118, a first subgroup of afirst plurality of edge subcarriers 115 a on the right and left sides ofthe inner subcarriers 118, and a second subgroup of a second pluralityof edge subcarriers 115 b on the right and left sides of the firstplurality of edge subcarriers 115 a. The length of the cyclic prefix 109of each subgroup may be reduced by a smaller amount as the subgroupsapproach the inner subcarriers 118. Different windowing functions maythen be applied to the different subgroups. For example, windows withsmoother transitions may be applied to edge subcarriers 115 in subgroupsthat are further from the inner subcarriers 118 with the transitionsoccurring over the windowing portion of each subgroup of edgesubcarriers 115.

In some implementations, a special windowing function may be applied toproduce asymmetrical spreading in the frequency domain. The asymmetryprovided by this special windowing function may be configured to producelarger right side-lobes and weak left side-lobes with different scalesor vice versa. For OFDM systems, the special windowing function may beapplied to the edge subcarriers 115 on the left side of the band toproduce weak left side lobes and large right side lobes (orright-dominant asymmetry). The right-dominant asymmetry of the specialwindowing function is gradually decreased towards the edge subcarriers115 located at the middle of the band. The windowing function issymmetrical only for the edge subcarriers 115 at the center of the band.For the edge subcarriers 115 on the right side of the band, the appliedwindowing function becomes left-dominant to produce weak right sidelobes and large left side lobes. Thus, by applying this specialwindowing function to the subcarriers in different scales ofsymmetrically, the energy of the side lobes of the subcarriers are keptin the band. Subsequently, the amplitude of the out-of-band side lobesis reduced.

Referring to FIG. 3, shown is a graphical representation of an exampleof a device 300 capable of handling OFDM signaling. OFDM has developedinto a popular scheme for wideband digital communication, whetherwireless or over copper wires, used in applications such as, e.g.,digital television and audio broadcasting, DSL broadband internetaccess, wireless networks, and 4G mobile communications. For example,the device 300 may be a cellular telephone or wireless base stationcapable of processing OFDM signaling. The device 200 receives or obtainsa series of OFDM symbols 103 from a source 303 such as, e.g., processingcircuitry that generates the series of OFDM symbols 103 or a data store.The source 303 may be internal to the device 300 or external to thedevice as illustrated in FIG. 3. In some implementations, the OFDMsymbols 103 may be from a combination of internal and/or externalsources 300. For example, OFDM symbols from two sources 303 may bemultiplexed for transmission by the device 300.

The OFDM symbols 103 are initially divided into groups (e.g., subgroupsor subblocks) of inner subcarriers 118 and edge subcarriers 115 by aseparator 306. For simplicity, the separation can be carried out in thefrequency domain. In the example of FIG. 3, the OFDM symbols 103 areseparated into a first group including a quantity of inner subcarriers118 and a second group including a quantity of edge subcarriers 115based upon the predefined S. In other implementations, the OFDM symbols103 may be divided into a plurality of edge subcarrier groups asillustrated in FIG. 2. The groups will be processed in parallel andrecombined for transmission by the transmitter or transceiver of thedevice 300.

Each group is then processed by initially performing an inverse fastFourier transformation (IFFT) 309. A cyclic prefix (CP) adder 312 thenadjusts the cyclic prefix to the groups of the OFDM symbols 103. Forexample, N^(edge) _(CP) may be added to the group of edge subcarriers115 and N_(CP) may be added added to the group of inner subcarriers 118.In other embodiments, the CP adder 312 may reduce the cyclic prefix ofthe corresponding group to the specified value of N^(edge) _(CP) and/orN_(CP). In some embodiments, the CP adder 312 may adjust a cyclicpostfix of the OFDM symbols 103. A windower 315 then windows the OFDMsymbol 103 using the specified window function. Combiner (or adder) 318sums the outputs of the windowers 315 to reform the OFDM symbol 103 fortransmission by the transmitter or transceiver of the device 300.

Since the inverse fast Fourier transformation (IFFT) and windowing arelinear operations, edge windowing method can be implemented by employingtwo branches for edge and inner subcarriers. As shown in FIG. 3,parallel branches are used for the IFFT and windowing of the innersubcarriers 118 and the IFFT and windowing for edge subcarriers 115.Edge windowing includes point-to-point operations such as point-to-pointmultiplication of windowing function and IFFT results and point-to-pointsummation of the results of the two branches. Thus, the edge windowingdoes not increase the computation complexity of the IFFT operation 309which is O(N log₂N).

The device 300 includes processing circuitry capable of implementing theseparator 306, IFFT 309, CP adder 312, windower 315, and combiner 318 asdescribed above. In various embodiments, the processing circuitry isimplemented as at least a portion of a microprocessor. The processingcircuitry may be implemented using one or more circuits, one or moremicroprocessors, application specific integrated circuits, dedicatedhardware, digital signal processors, microcomputers, central processingunits, field programmable gate arrays, programmable logic devices, statemachines, or any combination thereof. In yet other embodiments, theprocessing circuitry may include one or more software modules executablewithin one or more processing circuits. The processing circuitry mayfurther include memory configured to store instructions and/or code thatcauses the processing circuitry to execute data communication functions.

The performance of the edge windowing approach was investigated throughcomputer simulations. The simulations were carried out using araised-cosine windowing function, since the raised cosine windowingfunction can be widely utilized in OFDM based systems. For OFDM signalparameters, the following were used: N=1024, N_(CP)=64, T_(S)=66.7 μs,N_(G)=100, N_(W)32 32, N^(inner) _(W)=4. An ITU Vehicular A model wasutilized and a Rayleigh distribution was used in each channelrealization and normalized with a total power of the generated channelto 1. The simulations were performed over 5000 OFDM symbols and 20000different channel realizations.

Referring to FIG. 4, shown an example of the average error vectormagnitude (EVM) on subcarriers for different Sand N^(edge) _(CP) values.The impact of the edge windowing on the average EVM performance of eachsubcarrier for different S and N^(edge) _(CP) values is plotted. Thepower of the interference can be adjusted by changing the introducededge windowing parameters. The last tap of the ITU Vehicular A model wasat 2510 ns (or nearly 39 samples). Thus,if N^(edge) _(CP) is selected aslarger or equal than 39, the ISI/ICI will be avoided totally for any Svalue. If N^(edge) _(CP) decreases less than 39, ISI/ICI on edgesubcarriers 115 and only ICI on inner subcarriers 118 are observed. Theimpact of the ICI becomes weaker on inner subcarriers 118 as can be seenin FIG. 4. Thus, EVM becomes more severe on edge subcarriers 115. Inaddition, increasing S results in more EVM for the cases of N^(edge)_(CP)<39, since more edge subcarriers 115 lose the orthogonality betweeninner subcarriers 118.

Referring next to FIG. 5, shown are examples of the suppressionperformance of edge windowing relative to the non-windowed OFDM. Thesuppression performance of the proposed edge windowing and theconventional windowing relative to the non-windowed OFDM is compared atvarious frequencies away from the most edge subcarrier 115 (or thesubcarrier on the outer edge. The following parameters: N^(edge)_(CP)=32 (N^(edge) _(W)=36) are considered in FIG. 5( a) and N^(edge)_(CP)=16 (N^(edge) _(W)=52) are considered in FIG. 5( b). If Sincreases, the suppression performance of edge windowing increases asshown in both FIGS. 5( a) and 5(b). The proposed edge windowingapproaches the suppression performance of conventional windowing forevery frequency after S=300. On the other hand, by increasing N^(edge)_(W), edge windowing provides sharper spectral shaping compared to theconventional as in FIG. 5( b). The throughput with edge windowingincreases by 2.57% compared to the throughput with conventionalwindowing with these parameters.

The impact of the edge windowing parameters on spectral efficiency, sidelobe suppression and average EVM are summarized in TABLE 1 for a givenN_(CP). While increasing S provides more side lobe suppression, itcauses more average EVM on subcarriers. N^(edge) _(W) increases, moresuppression is achieved but more EVM is observed due to the lessN^(edge) _(CP). On the other hand, employing larger N^(inner) _(W)provides more side lobe suppression and less EVM while decreasing thespectral efficiency.

TABLE 1 Item Spectral Efficiency Supression Ave. EVM N^(edge) _(CP) ↑ S— ↑ ↑ — ↑ N^(edge) _(W) — ↑ ↑ ↓ ↑ N^(inner) _(W) ↓ ↑ ↓ —

As may be seen from the results of FIGS. 4 and 5, the proposed edgewindowing technique provides both spectral efficiency and side lobesuppression. Edge windowing introduces a new degree of freedom inspectral efficient side lobe suppression and controllable ISI/ICI. Bychanging the introduced parameter of edge windowing; suppressionperformance and spectral efficiency may be changed adaptively byintroducing a controllable interference. This degree of freedom may beexploited with a subcarrier based adaptive approach like adaptivemodulation, power control, and scheduling to improve the capacity andperformance of OFDM based wireless communication systems.

The impact of ISI and/or ICI due to the insufficient cyclic prefix 109of the edge subcarriers 115 may be reduced or eliminated by properscheduling of the subcarriers and exploiting the dependency of channeldispersive characteristics to the distance between a transmitter and areceiver of, e.g., cellular communications. User devices (e.g., mobilestations) that are closer to the base station have less dispersivechannels, thus allowing for use a shorter cyclic prefix 109 withoutadversely affecting ISI. User devices (e.g., mobile stations) locatednear a base station have less dispersive channels than users locatedfurther away. Because of this, nearby users require less of a cyclicprefix 109 than those users located at greater distances. By assigningthe inner subcarriers 118 to users that are further away from the basestation, ICI and ISI can be mitigated. For example, channels of userdevices that fall within (or are less than) a distance threshold may beassigned to edge subcarriers and channels of user devices that falloutside (or are greater than) the distance threshold may be assigned toinner subcarriers. The distance threshold may be determined based atleast in part upon the number of edge carriers (S) and the determineddistances of the user devices. The determined distance should be locatedto separate the all channels between the edge and inner subcarriers. Inother implementations, the subcarriers may be scheduled based upon theroot mean square (RMS) delay spread (T_(RMS) or T_(rms)) of the channel.

Consider the downlink of an OFDMA based system with a coverage radius ofR. A circular shape is considered rather than a hexagonal shape in orderto simplify the analysis. The base station is located at center of thecell and the locations of mobile stations are distributed uniformly. Thetransmitted OFDMA symbol 103 from the base station is given with theparameters of N available subcarriers, N_(CP) cyclic prefix size, T_(S)OFDMA symbol duration, and N_(G) guard subcarriers.

As discussed above, edge windowing for spectral shaping is based oncombining the windowing time with the cyclic prefix. In this way, noadditional windowing time is needed in the windowed carriers. Comparedto conventional windowing, where all the subcarriers are windowed asshown in FIG. 1( a), in the edge windowing only S edge subcarriers 115are utilized for windowing instead of using all subcarriers asillustrated in FIG. 1( b). FIG. 6 illustrates this relationship from atop down perspective. While the size of the cyclic extensions of thenon-windowed subcarriers remains as N_(CP), the size of the cyclicextensions of the windowed subcarriers is reduced to N^(S) _(CP). Then,the windowing is applied to the remaining part from the cyclicextensions of windowed subcarriers as N^(S) _(W)=N_(CP)−N^(S) _(CP)instead of using an additional windowing time N_(W). Therefore, edgewindowing eliminates the additional windowing time requirement of theconventional windowing.

For windowing, consider a raised cosine windowing function with thecharacteristics (in samples)

$\begin{matrix}{g_{n} = \left\{ \begin{matrix}{\frac{1}{2} + {\frac{1}{2}{\cos \left( {\pi + \frac{\pi \; n}{\beta_{W}N_{T}}} \right)}}} & {0 \leq n \leq {\beta_{W}N_{T}}} \\1 & {{\beta_{W}N_{T}} \leq n \leq N_{T}} \\{\frac{1}{2} + {\frac{1}{2}{\cos \left( {\pi - \frac{\pi \; n}{\beta_{W}N_{T}}} \right)}}} & {N_{T} \leq n \leq {\left( {\beta_{W} + 1} \right)N_{T}}}\end{matrix} \right.} & {{EQN}\mspace{14mu} (1)}\end{matrix}$

where β_(W) is the roll off factor (0≦β_(W)≦1) and N_(T) is the symbollength for the raised cosine function. Thus, while the parameters ofraised cosine windowing function are N_(T)=N+N^(S) _(CP), N^(S)_(W)=β^(S) _(W)(N+N^(S) _(CP)) for edge windowing, the same parametersare N_(T)=N+N_(CP), N_(W)=β_(W)(N+N_(CP)) for the conventionalwindowing. Note that β_(W)≦β^(S) _(W) when N_(W)≦N^(S) _(W). Thus, edgewindowing can introduce better side lobe suppression performance thanconventional windowing depending on the parameter of S.

Assuming that the power delay profile of the channel between the basestation and the mobile stations decays exponentially, the model of theexponential decaying may be given as:

$\begin{matrix}{{{P_{\exp}\lbrack k\rbrack} - {B\; ^{{- k}\; \alpha}}},{\alpha \equiv \frac{T_{s}}{N_{\tau_{0}}}}} & {{EQN}\mspace{14mu} (2)}\end{matrix}$

where k is the index for the tap, B and T₀ are the constants to beobtained to adjust the average power of channel. The summation of P[k]is set equal to 1. Hence, B is derived as:

$\begin{matrix}{{\sum\limits_{k = o}^{\infty}{P\lbrack k\rbrack}} = {{1->B} = {1 - {^{- \alpha}.}}}} & {{EQN}\mspace{14mu} (3)}\end{matrix}$

Since RMS delay spread (T_(RMS) or T_(rms)) of the channel can beobtained from the second order central moment of EQN. (2), bycalculating its inverse function, T₀ may be derived as:

$\begin{matrix}{{\tau_{0} = \frac{T_{rms}\beta}{2\; {\ln \left( {\frac{\beta}{2} + {1\sqrt{1 + \left( \frac{\beta}{2} \right)^{2}}}} \right)}}},{\beta \equiv {\frac{T_{s}}{{NT}_{rms}}.}}} & {{EQN}\mspace{14mu} (4)}\end{matrix}$

Also, consider that T_(RMS) depends on the distance between base stationand mobile station. The mathematical expression which relates T_(RMS)and the distance can be given as:

T_(rms)=T₁d^(ε)y   EQN (5)

where d is the distance between base station and mobile station inkilometers, ε is a distance coefficient lies between 0.5≦ε≦1, T₁ is themedian value of T_(RMS) at d=1 km, and y is a lognormal distributedrandom variable. The standard deviation of y lies as 2≦σ_(y)≦6 in dB.Thus, the distribution of T_(RMS) is also lognormal.

According to EQN. (5), the mobile stations nearby the base station haveless dispersive channels than the mobile stations located at fartherdistances. Therefore, the cyclic prefix size needed for the nearbymobile station is less than the one needed for the far mobile station.Edge windowing can exploit this feature with a frequency dependentscheduling capability of the OFDMA signals. For edge windowing, onescheduling approach is to group mobile stations with similar dispersioncharacteristics and to assign the group to the proper subcarriers whichdo not generate ISI. Three fundamental scheduling strategies may beemployed for the edge windowing: random scheduling, ranging basedscheduling and, T_(RMS) based scheduling. The scheduling may beimplemented by a scheduler 321 included in the device 300 of FIG. 3. Thedevice 300 can include processing circuitry capable of implementing thescheduler 321.

FIG. 7 illustrates the different scheduling strategies. Beginning withFIG. 7( a), shown is a random scheduling of the subcarriers where thedispersion characteristics and the distance from the base station arenot considered. Random scheduling strategy was considered to observe theimpact of ignoring scheduling requirements of the edge windowing. Inthis scheduling strategy, all the spectrum resources are distributedrandomly to the mobile stations as in FIG. 7( a). Thus, the channeldispersion characteristics and the distance between mobile stations andbase station were not considered for scheduling decision. However, ISIand/or ICI may be reduced by assigning mobile stations to the edgesubcarriers 115 based upon distance and/or T_(RMS).

FIG. 7( b) illustrates scheduling of the subcarriers using estimateddistance (or range) to the mobile station. The nearest mobile stationsare located in the center of the edge subcarriers 115 and the mobilestations farthest away are located in the center of the innersubcarriers 118. Such a grouping does not guarantee grouping mobilestations with low T_(RMS). Ranging based scheduling exploits therelation between the distance and dispersion level given in EQN. (5).Thus, it is performed after estimating the distances of the mobilestations relative to the base stations with ranging operations. In theranging based scheduling approach, the nearby mobile stations areassigned to the windowed edge subcarriers 115, and the far away mobilestations are assigned to non-windowed inner subcarriers 118 as shown inFIG. 7( b). While the spectrum resources located at the center of theband of the windowed edge subcarriers 115 are employed for the nearestmobile station, the spectrum resources located at the center of OFDMband (and thus the center of the inner subcarriers 118) are used for thefarthest mobile station.

It should be noted that ranging based scheduling does not guarantee agrouping of the mobile stations with low T_(RMS). Therefore, the mobilestations scheduled to subcarriers at the edges of the windowedsubcarriers (e.g., mobile stations located at middle distances) canobserve severe ISI because of the having probability of high T_(RMS).Also, since the mobile stations are distributed uniformly in the cellarea, the distribution of the distance between the mobile stations andbase station is obtained as

$\begin{matrix}{{{f_{r}(r)} = \frac{2r}{R^{2}}},{0 \leq r \leq {R.}}} & {{EQN}\mspace{14mu} (6)}\end{matrix}$

Thus, the expected number of the mobile stations at farther distances ishigher than the number of the closer ones. Therefore, increasing S alsoincreases the probability of having ISI on these subcarriers.

T_(RMS) based scheduling applies a scheduling approach that considersthe T_(RMS) parameters of each of the mobile stations' channels insteadof their distances to the base station. FIG. 7( c) illustratesscheduling of the subcarriers using T_(RMS) of the mobile station.Similar to distance, mobile stations with the lowest T_(RMS) are locatedin the center of the edge subcarriers 115 and the mobile stations withthe highest T_(RMS) are located in the center of the inner subcarriers118. As shown in FIG. 7( c), the mobile stations with low T_(RMS) valuesand mobile stations with high T_(RMS) values are scheduled to thewindowed edge subcarriers 115 and non-windowed inner subcarriers 118,respectively. While the spectrum resources located at the center of theband of the windowed edge subcarriers 115 are utilized for the mobilestation with the lowest T_(RMS), the spectrum resources located at thecenter of the OFDM band (and thus the center of the inner subcarriers118) are assigned for the mobile station with the highest T_(RMS). Ascan be seen, such a grouping does not guarantee grouping the nearestmobile stations.

For T_(RMS) based scheduling, the base station uses the channeldispersion information of each mobile station. In most of the wirelesscommunication cases (e.g., Wi-Fi, LTE, etc.), the base station hasability to extract the downlink channels of the mobile stations. Thus,it is reasonable to have T_(RMS) information of each mobile station atthe base station. Also, it should be noted that T_(RMS) is a randomvariable depending on the distance between mobile station and the basestation as in EQN. (5). Thus, T_(RMS) scheduling approach does notguarantee that the mobile stations are ordered on the spectral resourcesconsidering their distances as shown in FIG. 7( c). In someimplementations, a combination of distance and T_(RMS) may be used forgrouping subcarriers.

The performance of edge windowing along with aforementioned schedulingstrategies was investigated through computer simulations. Consider thatN=1024, N_(CP)=128, T_(S)=66.7 μs, N_(G)=80 for OFDMA symbol parametersand T₁=1 μs, ε=0.5, and σ_(y)=2 dB for the channel parameters for anurban environment. Therefore, edge windowing parameters become 0≦N^(S)_(CP)≦128 and 0≦S≦432 from this set of simulation parameters. Thesimulations also considered 12 subcarriers (one resource block) permobile station and 72 mobile stations which are distributed uniformly ina cell radius of R=1000 m. All results were obtained over 50 OFDMAsymbols per channel and 300 different channels per mobile station. Allsimulations were performed with the same set of parameters in order toobtain a reasonable set of edge windowing parameters. Initially, theside lobe suppression and throughput performances of edge windowing andconventional windowing are compared. Then, the impact of scheduling onthe average EVM on subcarriers and other EVM statistics is examined.

The side lobe suppression performance of the edge windowing depends uponthe both parameters of N^(S) _(W) and S. A value of N_(W)=64 wasselected for conventional windowing and the side lobe suppressionperformances of both windowing techniques relative to the non-windowedOFDMA symbol 103 on 136.3 kHz away from the farthest edge subcarrier 115was plotted as shown in FIG. 8. Edge windowing offers better side lobesuppression than conventional windowing depending on S when β^(S) _(W)is larger than the β_(W) (i.e. N^(S) _(W)≧N_(W)). Since the windowing isapplied to only S edge subcarriers 115, increasing S helps to improvethe side lobe suppression performance of edge windowing. In FIG. 8, edgewindowing performance 803 approaches to the side lobe suppressionperformance of the conventional windowing 806 with parameters of N^(S)_(W)=64 and S=192.

Edge windowing eliminates the need of additional windowing time. Thus,the throughput of the system with edge windowing is higher than thesystem with the conventional windowing. The increment on the throughput(AR) can be calculated in percent as:

$\begin{matrix}{{\Delta \; R} = {100{\frac{N_{W}}{N + N_{CP}}.}}} & {{EQN}\mspace{14mu} (7)}\end{matrix}$

Considering the simulation parameters, edge windowing provided a 5.6%increment on throughput relative to the system with conventionalwindowing.

Referring now to FIG. 9, shown are the average T_(RMS) values of thechannels on each resource block (N^(S) _(W)=64 and S=192). Since randomscheduling 903 does not consider the channel dispersion characteristicsand the distances, average T_(RMS) does not vary over the resourceblocks. For ranging based scheduling 906, average T_(RMS) decreases onthe resource blocks where the windowing is applied and it increases atthe middle of the OFDMA band. Since T_(RMS) based scheduling 909exploits the knowledge of T_(RMS) of each mobile station's channel, itprovides a better grouping of the mobile station with the same T_(RMS).Thus, the average T_(RMS) values with T_(RMS) based scheduling 909 areless than the ones with ranging based scheduling 906 at the center ofthe band of the windowed edge subcarriers 115. T_(RMS) based scheduling909 also provides larger average T_(RMS) values at the middle of theOFDM band.

In order to investigate the impact of the scheduling, the average EVM oneach subcarriers and average EVM at different distances for different Svalues (N^(S) _(W)=64) were simulated and plotted in FIGS. 10A-10C and11A-11C, respectively.

If the scheduling is performed randomly, the average EVM on the windowedsubcarriers become drastically high compared to the non-windowedsubcarriers as shown in FIG. 10A. Since the cyclic extension size of thewindowed edge subcarriers 115 are insufficient for the mobile stationswhich have high dispersive channels, ISI reduces the EVM performances ofthese subcarriers significantly. It may especially impact the mobilestations located at farther distances. As shown in FIG. 11A, the mobilestations located at the edge of the cell observe high average EVM of1.2%. It indicates that the average EVM increases rapidly when thedistance between the mobile station and base station is increasing.Also, it shows the dependency of average EVM to the S parameter of edgewindowing.

If the scheduling is performed considering the distance between themobile stations and the base station, the average EVM raises on thesubcarriers along the sides (or edges) of the windowed edge subcarriers115 as shown in FIG. 10B. It is clear that the nearby mobile stationswhich are assigned to the center subcarriers of the windowed edgesubcarriers 115 do not observe ISI since their channels are expected tobe less dispersive. However, the mobile stations which are scheduled tothe subcarriers along the sides of the windowed edge subcarriers 115 canobserve severe ISI due to their distances. EQN. (6) shows that theaverage number of the mobile stations increases linearly with thedistance. Since more mobile stations are located at the large distances,more mobile station have the channels with high T_(RMS) as shown in FIG.9. Therefore, the mobile stations scheduled to the subcarriers along thesides of the windowed edge subcarriers 115 can observe high EVM withranging based scheduling. This issue is also illustrated in FIG. 11B.Since ranging based scheduling strategy assigns the subcarriers alongthe sides of the windowed edge subcarriers 115 to the mobile stations atmiddle distances, these mobile stations observe high EVM. For instance,the simulation results of FIG. 11B indicated that the mobile stations at600 m away from the base station have higher average EVM than the otherdistances when S=192.

If the base station schedules the mobile stations considering theT_(RMS) of each of the mobile station's channels, the average EVMperformance on subcarriers increases significantly as shown in FIG. 10C.Since T_(RMS) based scheduling provides better grouping of the mobilestations with the same T_(RMS) than the ranging based scheduling, itoffers better average EVM performance. However, using higher S values(e.g., S≧300) impacts the EVM on the subcarriers along the sides of thewindowed edge subcarriers 115. Also, increasing S degrades the averageEVM of the far mobile stations because they have highly dispersivechannels. The relation between the distance of the mobile station andaverage EVM is given for different S values is illustrated in FIG. 11C.If S=192 is considered for the system design, average EVM does notexceed 0.25% in both FIGS. 10C and 11C.

According to simulation results given in FIGS. 10A-10C and 11A-11C, theedge windowing along with T_(RMS) based scheduling is superior than theother scheduling strategies when N^(S) _(W)=64 and S=192. For N^(S)_(W)=64 and S=192, the statistical distributions of EVM on thesubcarriers were analyzed in FIG. 12. The lower CDF bound of EVM onsubcarriers is given in FIG. 12( a) by considering the worst caseprobability for a given EVM value on each subcarrier. Thus, the CDFcurve of EVM for each subcarrier is always better than the curves givenin FIG. 12( a). Also, the average of the all CDF curves of EVM onsubcarriers is given in FIG. 12( b) in order to evaluate the impact ofthe scheduling. As shown in FIG. 12( b), whereas the worst caseprobability of EVM below 0.5% is 79% for both random scheduling andranging based scheduling, it is 96% for T_(RMS) based scheduling. Evenif the worst case probabilities are the same for both ranging basedscheduling and random scheduling, the probability values are differentin average case. As shown in FIG. 12( b), while the probability is 91%for ranging based scheduling, it is 87% for random scheduling. Also, theprobability of 98% is obtained for T_(RMS) based scheduling.

The analysis indicates that edge windowing along with a properscheduling provides both side lobe suppression and increments on thethroughput with tolerable EVM on subcarriers. Ranging based schedulingprovides improvement on EVM performance compared to the randomscheduling, however ranging based scheduling does not guarantee groupingof the mobile stations with the same T_(RMS). T_(RMS) based schedulingalong with the edge windowing provides an improvement on EVMperformances by guarantying such a grouping. Considering the simulationparameters, the worst case probability of EVM below 0.5% on a subcarrieris 96% with T_(RMS) based scheduling when N^(S) _(W)=64, S=192. Also,edge windowing provided a 5.6% increment on throughput compared to theconventional windowing.

Referring next to FIG. 13A, shown is a flow chart illustrating anexample of edge windowing of OFDM symbols 103. Beginning with 1303, oneor more OFDM symbols 103 are received. The OFDM symbols 103 can includea cyclic prefix and a data portion. The subcarriers of the OFDM symbol103 may have been scheduled to reduce ISI and ICI as discussed above.The subcarriers may be scheduled based at least in part upon the T_(RMS)and/or the distance of corresponding user devices. In 1306, the cyclicprefix can be adjusted for a predefined quantity of edge subcarriers115. For example, the cyclic prefix size (N_(CP)) may be reduced for aplurality of edge subcarriers 115 in the OFDM symbol to obtain an edgewindowing portion (N^(edge) _(W)) within the cyclic prefix the OFDMsymbol 103. A windowing function may then be applied to the edgesubcarriers 115 in 1309 to reduce side lobes. In some implementations,an inner windowing portion (N^(inner) _(W)) may be obtained within thecyclic prefix and a second windowing function may be applied to theinner subcarriers 118 of the OFDM symbol 103. The transition of thewindowing function(s) occurs within the windowing portion(s) of thecyclic prefix. The process may be repeated for each of a series of OFDMsymbols. The processed OFDM symbol may then be provided fortransmission.

Referring next to FIG. 13B, shown is a flow chart illustrating anexample of scheduling subcarriers of OFDM symbols 103. Beginning with1312, a RMS delay spread associated with one or more mobile stations (oruser devices) and/or a distance between the one or more mobile stationsand a base station is determined. In 1315, subcarriers of the OFDMsymbols are scheduled to the one or more mobile stations based upon thedetermination. For example, scheduling of the subcarriers may be basedat least in part upon the RMS delay spread and/or the distance.

With reference to FIG. 14, shown is a schematic block diagram of anexample of the device 300 of FIG. 3 in accordance with variousembodiments of the present disclosure. The device 300 includes at leastone processor circuit, for example, having a processor 1403 and a memory1406, both of which are coupled to a local interface 1409. The device300 may include one or more interface(s) that comprise processingcircuitry for supporting Wi-Fi communications such as, e.g., IEEE 802.11a/b/g/n or other wireless communication protocols, and/or cellularcommunications such as, e.g., LTE, WiMAX, WCDMA, HSDPA, or otherwireless communication protocols that utilize OFDM. In variousembodiments, the processing circuitry is implemented as at least aportion of a microprocessor. The processing circuitry may be implementedusing one or more circuits, one or more microprocessors, applicationspecific integrated circuits, dedicated hardware, digital signalprocessors, microcomputers, central processing units, field programmablegate arrays, programmable logic devices, state machines, or anycombination thereof. In yet other embodiments, the processing circuitrymay include one or more software modules executable within one or moreprocessing circuits. The processing circuitry may further include memoryconfigured to store instructions and/or code that causes the processingcircuitry to execute data communication functions. The local interface1409 may comprise, for example, a data bus with an accompanyingaddress/control bus or other bus structure as can be appreciated.

Stored in the memory 1406 may be both data and several components thatare executable by the processor 1403. In particular, stored in thememory 1406 and executable by the processor 1403 may be a separator 306,an IFFT 309, a CP adder 312, a windower 315, a scheduler 321, andpotentially other applications and device interfaces. In addition, anoperating system may be stored in the memory 1406 and executable by theprocessor 1403. In some cases, the processor 1403 and memory 1406 may beintegrated as a system-on-a-chip. In other embodiments, the separator306, IFFT 309, CP adder 312, windower 315, and/or scheduler 321 may beimplemented in firmware or dedicated hardware.

It is understood that there may be other applications that are stored inthe memory 1406 and are executable by the processor 1403 as can beappreciated. Where any component discussed herein is implemented in theform of software, any one of a number of programming languages may beemployed such as, for example, C, C++, C#, Objective C, Java®,JavaScript®, Perl, PHP, Visual Basic®, Python®, Ruby, Delphi®, Flash®,or other programming languages.

A number of software components are stored in the memory 1406 and areexecutable by the processor 1403. In this respect, the term “executable”means a program file that is in a form that can ultimately be run by theprocessor 1403. Examples of executable programs may be, for example, acompiled program that can be translated into machine code in a formatthat can be loaded into a random access portion of the memory 1406 andrun by the processor 1403, source code that may be expressed in properformat such as object code that is capable of being loaded into a randomaccess portion of the memory 1406 and executed by the processor 1403, orsource code that may be interpreted by another executable program togenerate instructions in a random access portion of the memory 1406 tobe executed by the processor 1403, etc. An executable program may bestored in any portion or component of the memory 1406 including, forexample, random access memory (RAM), read-only memory (ROM), hard drive,solid-state drive, USB flash drive, memory card, optical disc such ascompact disc (CD) or digital versatile disc (DVD), floppy disk, magnetictape, or other memory components.

The memory 1406 is defined herein as including both volatile andnonvolatile memory and data storage components. Volatile components arethose that do not retain data values upon loss of power. Nonvolatilecomponents are those that retain data upon a loss of power. Thus, thememory 1406 may comprise, for example, random access memory (RAM),read-only memory (ROM), hard disk drives, solid-state drives, USB flashdrives, memory cards accessed via a memory card reader, floppy disksaccessed via an associated floppy disk drive, optical discs accessed viaan optical disc drive, magnetic tapes accessed via an appropriate tapedrive, and/or other memory components, or a combination of any two ormore of these memory components. In addition, the RAM may comprise, forexample, static random access memory (SRAM), dynamic random accessmemory (DRAM), or magnetic random access memory (MRAM) and other suchdevices. The ROM may comprise, for example, a programmable read-onlymemory (PROM), an erasable programmable read-only memory (EPROM), anelectrically erasable programmable read-only memory (EEPROM), or otherlike memory device.

Also, the processor 1403 may represent multiple processors 1403 and thememory 1406 may represent multiple memories 1406 that operate inparallel processing circuits, respectively. In such a case, the localinterface 1409 may be an appropriate network that facilitatescommunication between any two of the multiple processors 1403, betweenany processor 1403 and any of the memories 1406, or between any two ofthe memories 1406, etc. The local interface 1409 may comprise additionalsystems designed to coordinate this communication, including, forexample, performing load balancing. The processor 1403 may be ofelectrical or of some other available construction.

Although the separator 306, IFFT 309, CP adder 312, windower 315,scheduler 321, and other various systems described herein may beembodied in software or code executed by general purpose hardware, as analternative the same may also be embodied in dedicated hardware,firmware, or a combination of software/general purpose hardware anddedicated hardware. If embodied in dedicated hardware, each can beimplemented as a circuit or state machine that employs any one of or acombination of a number of technologies. These technologies may include,but are not limited to, discrete logic circuits having logic gates forimplementing various logic functions upon an application of one or moredata signals, application specific integrated circuits havingappropriate logic gates, or other components, etc. Such technologies aregenerally well known by those skilled in the art and, consequently, arenot described in detail herein.

The flowcharts of FIGS. 13A and 13B show the functionality and operationof an implementation of portions of the separator 306, IFFT 309, CPadder 312, windower 315, and/or scheduler 321. If embodied in software,each block may represent a module, segment, or portion of code thatcomprises program instructions to implement the specified logicalfunction(s). The program instructions may be embodied in the form ofsource code that comprises human-readable statements written in aprogramming language or machine code that comprises numericalinstructions recognizable by a suitable execution system such as aprocessor 1403 in a computer system or other system. The machine codemay be converted from the source code, etc. If embodied in hardware,each block may represent a circuit or a number of interconnectedcircuits to implement the specified logical function(s).

Although the flowcharts of FIGS. 13A and 13B show a specific order ofexecution, it is understood that the order of execution may differ fromthat which is depicted. For example, the order of execution of two ormore blocks may be scrambled relative to the order shown. Also, two ormore blocks shown in succession in FIGS. 13A and 13B may be executedconcurrently or with partial concurrence. Further, in some embodiments,one or more of the blocks shown in FIGS. 13A and 13B may be skipped oromitted. In addition, any number of counters, state variables, warningsemaphores, or messages might be added to the logical flow describedherein, for purposes of enhanced utility, accounting, performancemeasurement, or providing troubleshooting aids, etc. It is understoodthat all such variations are within the scope of the present disclosure.

Also, any logic or application described herein, including the separator306, IFFT 309, CP adder 312, windower 315, and/or scheduler 321 thatcomprises software or code can be embodied in any non-transitorycomputer-readable medium for use by or in connection with an instructionexecution system such as, for example, a processor 1403 in a computersystem or other system. In this sense, the logic may comprise, forexample, statements including instructions and declarations that can befetched from the computer-readable medium and executed by theinstruction execution system. In the context of the present disclosure,a “computer-readable medium” can be any medium that can contain, store,or maintain the logic or application described herein for use by or inconnection with the instruction execution system.

The computer-readable medium can comprise any one of many physical mediasuch as, for example, magnetic, optical, or semiconductor media. Morespecific examples of a suitable computer-readable medium would include,but are not limited to, magnetic tapes, magnetic floppy diskettes,magnetic hard drives, memory cards, solid-state drives, USB flashdrives, or optical discs. Also, the computer-readable medium may be arandom access memory (RAM) including, for example, static random accessmemory (SRAM) and dynamic random access memory (DRAM), or magneticrandom access memory (MRAM). In addition, the computer-readable mediummay be a read-only memory (ROM), a programmable read-only memory (PROM),an erasable programmable read-only memory (EPROM), an electricallyerasable programmable read-only memory (EEPROM), or other type of memorydevice.

It should be emphasized that the above-described embodiments of thepresent disclosure are merely possible examples of implementations setforth for a clear understanding of the principles of the disclosure.Many variations and modifications may be made to the above-describedembodiment(s) without departing substantially from the spirit andprinciples of the disclosure. All such modifications and variations areintended to be included herein within the scope of this disclosure andprotected by the following claims.

It should be noted that ratios, concentrations, amounts, and othernumerical data may be expressed herein in a range format. It is to beunderstood that such a range format is used for convenience and brevity,and thus, should be interpreted in a flexible manner to include not onlythe numerical values explicitly recited as the limits of the range, butalso to include all the individual numerical values or sub-rangesencompassed within that range as if each numerical value and sub-rangeis explicitly recited. To illustrate, a concentration range of “about0.1% to about 5%” should be interpreted to include not only theexplicitly recited concentration of about 0.1 wt % to about 5 wt %, butalso include individual concentrations (e.g., 1%, 2%, 3%, and 4%) andthe sub-ranges (e.g., 0.5%, 1.1%, 2.2%, 3.3%, and 4.4%) within theindicated range. The term “about” can include traditional roundingaccording to significant figures of numerical values. In addition, thephrase “about ‘x’ to ‘y’” includes “about ‘x’ to about ‘y’”.

Therefore, at least the following is claimed:
 1. A method for edgewindowing of orthogonal frequency division multiplexing symbols,comprising: receiving, by processing circuitry, an orthogonal frequencydivision multiplexing symbol including a cyclic prefix and a dataportion; obtaining, by the processing circuitry, an edge windowingportion in the cyclic prefix by reducing a cyclic prefix size for apredefined quantity of edge subcarriers in the orthogonal frequencydivision multiplexing symbol; and reducing, by the processing circuitry,side lobes of the orthogonal frequency division multiplexing symbol byapplying a windowing function to the predefined quantity of edgesubcarriers.
 2. The method of claim 1, wherein a transition of thewindowing function occurs within the windowing portion.
 3. The method ofclaim 1, further comprising obtaining an inner windowing portion byreducing the cyclic prefix size for a predefined quantity of innersubcarriers.
 4. The method of claim 1, wherein obtaining the edgewindowing portion includes reducing the cyclic prefix size of thepredefined quantity of edge subcarriers on a first side and a secondside of the orthogonal frequency division multiplexing symbol.
 5. Themethod of claim 4, further comprising: obtaining a second edge windowingportion by reducing the cyclic prefix size for a second predefinedquantity of edge subcarriers on the first side and the second side ofthe orthogonal frequency division multiplexing symbol; and reducing theside lobes of the orthogonal frequency division multiplexing symbol byapplying a second windowing function to the second predefined quantityof edge subcarriers.
 6. The method of claim 1, further comprisingtransmitting the orthogonal frequency division multiplexing symbolincluding the windowed edge subcarriers from a base station.
 7. Themethod of claim 6, further comprising transmitting a series oforthogonal frequency division multiplexing symbols from the basestation, each orthogonal frequency division multiplexing symbolincluding windowed edge subcarriers.
 8. The method of claim 1, furthercomprising scheduling subcarriers of the orthogonal frequency divisionmultiplexing symbol based upon a distance from a user device to a basestation.
 9. The method of claim 8, wherein scheduling the subcarriersincludes assigning channels of user devices that are within a distancethreshold to edge subcarriers of the orthogonal frequency divisionmultiplexing symbol and assigning channels of user devices that areoutside the distance threshold to inner subcarriers of the orthogonalfrequency division multiplexing symbol.
 10. The method of claim 1,further comprising scheduling subcarriers of the orthogonal frequencydivision multiplexing symbol based upon a root mean square delay spreadof a channel.
 11. The method of claim 10, wherein scheduling thesubcarriers includes assigning user devices with lower root mean squaredelay spread to edge subcarriers of the orthogonal frequency divisionmultiplexing symbol and assigning user devices with higher root meansquare delay spread to inner subcarriers of the orthogonal frequencydivision multiplexing symbol
 12. The method of claim 1, furthercomprising producing asymmetrical spreading of the side lobes byapplying the windowing function.
 13. A device, comprising: a separatorconfigured to divide subcarriers of an orthogonal frequency divisionmultiplexing symbol into a first subcarrier group comprising edgesubcarriers of the orthogonal frequency division multiplexing symbol anda second subcarrier group comprising inner subcarriers of the orthogonalfrequency division multiplexing symbol; a first CP adder configured toobtain a windowing portion within the cyclic prefix by adjusting acyclic prefix size of the first subcarrier group; and a first windowerconfigured to reduce side lobes of the orthogonal frequency divisionmultiplexing symbol by applying a windowing function to the firstsubcarrier group.
 14. The device of claim 13, comprising a combinerconfigured to combine the first subcarrier group and second subcarriergroup.
 15. The device of claim 14, comprising: a second CP adderconfigured to obtain a second windowing portion within the cyclic prefixby adjusting a cyclic prefix size of the second subcarrier group; and asecond windower configured to apply a second windowing function to thesecond subcarrier group.
 16. The device of claim 13, wherein theseparator is further configured to divide the subcarriers into a thirdsubcarrier group that includes subcarriers between the first and secondsubcarrier groups.
 17. The device of claim 13, wherein the deviceincludes a base station.
 18. A method, comprising: determining, byprocessing circuitry, a root mean square delay spread for each channelof a plurality of mobile stations in communication with a base station;and scheduling, by the processing circuitry, subcarriers of a series oforthogonal frequency division multiplexing symbols to the plurality ofmobile stations based at least in part upon the corresponding root meansquare delay spread.
 19. The method of claim 18, wherein schedulingsubcarriers includes assigning the channel with the highest root meansquare delay spread to a center subcarrier of the orthogonal frequencydivision multiplexing symbols.
 20. The method of claim 18, furthercomprising: determining a distance from the base station to each of theplurality of mobile stations; and scheduling the subcarriers of theseries of orthogonal frequency division multiplexing symbols based uponthe corresponding root mean square delay spread and the correspondingdistance.